Neutrosophic filters in BE-algebras

Inthispaper, weintroducethenotionof(implicative)neutrosophicfilters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BE-algebras these notions are equivalent

Neutrosophic Vague Binary G-subalgebra of G-algebra

Nowadays, human society is using artificial intelligence in a large manner so as to upgrade the present existing applicational criteria’s and tools. Logic is the underlying principle to these works. Algebra is inevitably inter-connected with logic. Hence its achievements to the scientific research outputs have to be addressed. For these reasons, nowadays, research on various algebraic structures are going on wide. Crisp set has also got developed in a parallel way in the forms as fuzzy, intuitionistic fuzzy, rough, vague, neutrosophic, plithogenic etc. Sets with one or more algebraic operations will form different new algebraic structures for giving assistance to these logics, which in turn acts to as, a support to artificial intelligence. BCH/BCI/BCK- are some algebras developed in the first phase of algebraic development output. After that, so many outputs got flashed out, individually and in combinations in no time. Q- algebra and QS –algebra are some of these and could be showed as such kind of productions. G- algebra is considered as an extension to QS – algebra. In this paper neutrosophic vague binary G – subalgebra of G – algebra is generated with example. Notions like, 0 – commutative G - subalgebra, minimal element, normal subset etc. are investigated. Conditions to define derivation and regular derivation for this novel concept are clearly presented with example. Constant of G – algebra can’t be treated as the identity element, generally. In this paper, it is well explained with example. Cosets for neutrosophic vague binary G – subalgebra of G - algebra is developed with proper explanation. Homomorphism for this new concept has been also got commented. Its kernel, monomorphism and isomorphism are also have discussed with proper attention

Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures

Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures

NeutroAlgebra of Neutrosophic Triplets using {Zn, x}

Smarandache in 2019 has generalized the algebraic structures to NeutroAlgebraic structures and AntiAlgebraic structures. In this paper, authors, for the first time, define the NeutroAlgebra of neutrosophic triplets group under usual+ and x, built using {Zn, x}, n a composite number, 5 \u3c n \u3c oo, which are not partial algebras. As idempotents in Zn alone are neutrals that contribute to neutrosophic triplets groups, we analyze them and build NeutroAlgebra of idempotents under usual + and x, which are not partial algebras. We prove in this paper the existence theorem for NeutroAlgebra of neutrosophic triplet groups. This proves the neutrals assocaited with neutrosophic triplet groups in { Zn, X} under product is a NeutroAlgebra of triplets. We also prove the non-existence theorem of NeutroAlgebra for neutrosophic triplets in case of Zn when n = 2p, 3p and 4p (for some primes p). Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained

Applications of (Neutro/Anti)sophications to Semihypergroups

A hypergroup, as a generalization of the notion of a group, was introduced by F. Marty in 1934. The first book in hypergroup theory was published by Corsini. Nowadays, hypergroups have found applications to many subjects of pure and applied mathematics, for example, in geometry, topology, cryptography and coding theory, graphs and hypergraphs, probability theory, binary relations, theory of fuzzy and rough sets and automata theory, physics, and also in biological inheritance

Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures

NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited)

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry

NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited)

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system and from any type of geometry. Generally, instead of a classical geometric Axiom, one may take any classical geometric Theorem from any axiomatic system and from any type of geometry, and transform it by NeutroSophication or AntiSophication into a NeutroTheorem or AntiTheorem respectively in order to construct a NeutroGeometry or AntiGeometry. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world